## Copyright (C) 2002 André Carezia
##
## This program is free software; you can redistribute it and/or modify
## it under the terms of the GNU General Public License as published by
## the Free Software Foundation; either version 2 of the License, or (at
## your option) any later version.
##
## This program is distributed in the hope that it will be useful, but
## WITHOUT ANY WARRANTY; without even the implied warranty of
## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
## General Public License for more details.
##
## You should have received a copy of the GNU General Public License
## along with this program; If not, see <http://www.gnu.org/licenses/>.

## Usage:  cheb (n, x)
##
## Returns the value of the nth-order Chebyshev polynomial calculated at
## the point x. The Chebyshev polynomials are defined by the equations:
##
##           / cos(n acos(x),    |x| <= 1
##   Tn(x) = |
##           \ cosh(n acosh(x),  |x| > 1
##
## If x is a vector, the output is a vector of the same size, where each
## element is calculated as y(i) = Tn(x(i)).

## Author:  André Carezia <acarezia@uol.com.br>
## Description:  Value of the Chebyshev polynomials

function T = cheb (n, x)
  if (nargin != 2)
    usage ("cheb (n, x)");
  endif
  
  if !(isscalar (n) && (n == round(n)) && (n >= 0))
    error ("cheb: n has to be a positive integer");
  endif

  if (max(size(x)) == 0)
    T = [];
  endif
				# avoid resizing latencies
  T = zeros(size(x));
  
  ind = x<=1;
  if (max(size(ind)))
    T(ind) = cos(n*acos(x(ind)));
  endif

  ind = x>1;
  if (max(size(ind)))
    T(ind) = cosh(n*acosh(x(ind)));
  endif

  T = real(T);
end

